The upper half of an inclined plane with inclination `phi` is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

Options

A. `mu=2 tan theta`
B. `mu= tan theta`
C. `mu=(2)/(tan theta)`
D. `mu=(1)/(tan theta)`

Answer

A

Explanation

(a) `v^(2)=2a_(1)s(a_(1)=g sin theta)`
`0=v^(2)-2a_(2)s(a^(2)=mu g cos theta-g sin theta)`
From these two equations we see that `a_(1)=a_(2)`
`implies" " g sin theta=mu g cos theta-g sin theta implies 2 tan theta =mu`